Sample Lesson Plan: Finding the Area of a Composite FigureCRISALDO CORDURA
This Learning Plan is open to be corrected or enhanced. This is just a sample of Lesson plan that will be used for online class of Mathematics 6: Module 6
DISCLAIMER: Some photos are not owned by the presenter. it was taken from various sites on Google.
Sample Lesson Plan: Finding the Area of a Composite FigureCRISALDO CORDURA
This Learning Plan is open to be corrected or enhanced. This is just a sample of Lesson plan that will be used for online class of Mathematics 6: Module 6
DISCLAIMER: Some photos are not owned by the presenter. it was taken from various sites on Google.
In this module, you will learn about formulas of different geometrical shapes in 2 and 3 dimensions. It has practice problems with solutions so that you can learn about how certain problems are to be approached and to be solved.
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Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
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Instructional Materials in Mathematics
1.
2. Topic Slide No.
Operations of Signed Numbers 6
Fraction 11
Operations in Algebraic Expressions 16
Plane Figures PPT 22
Polygons (Geoboard) 41
Area and Perimeter of Irregular Polygons PPT 46
Platonic Solids PPT 60
Platonic and Achimedean Solid Model 84
Circle 89
Contents
3. •Instructional materials are devices that assist the
facilitator in the teaching-learning process.
•Instructional materials are not self-supporting;
they are supplementary training devices
•This includes power point presentations, books,
articles, manipulatives and visual aids.
4. Values and Importance
•To help clarify important concepts
•To arouse and sustain student’s interests
•To give all students in a class the
opportunity to share experiences necessary
for new learning
•To help make learning more permanent
7. Number Line Route
Objectives:
The operations of signed numbers instructional
material will be able to:
• Define signed numbers
• Apply the operations of signed numbers using
number line
• Visualize the operations of signed numbers
• Manipulate the operations of signed numbers
• Value the importance of signed numbers through
cultural integration
8. How to use:
• Introduce the positive and negative numbers in a number line. Write
the values in the number line using whiteboard pen on the octagon-
shaped space; positive numbers on the right of the zero and negative
numbers on the left of the zero.
• Move the jeepney on the desired “JEEPNEY STOP”. Attach on the
jeepney stop post the “STOP 1” card.
For addition
Move the jeepney forward if you want to add a positive number.
Move the jeepney backward if you will add a negative number
For subtraction
Move the jeepney backward if you want to subtract a positive
number. Move the jeepney forward if you want to subtract a negative
number.
12. Fraction
Tiles
Objectives:
The fraction tiles instructional material will be
able to:
• Define fraction numbers
• Apply the operations of fraction numbers using
tiles
• Visualize the operations of fraction numbers
• Manipulate the operations of fraction numbers
• Value the importance of fraction numbers
through daily encounter when buying
13. How to use:
• Place a number of tiles on the pink board that corresponds a
whole/denominator. (ex. 5 tiles corresponds a whole)
• On the top of the tiles, place the another tiles with another
color that will correspond the part/numerator. (ex. 2 tiles,
makes 2/5)
For addition
Place a same colored tiles of the numerator tiles next to
the numerator tiles, then count the total numerator tiles.
For addition
Get a number of numerator tiles, then count the
remaining numerator tiles
17. Algebra
Tiles
Objectives:
The algebra tiles instructional material will be able
to:
• To represent positive and negative integers using
Algebra Tiles.
• Manipulate operations of positive and negative
integers using Algebra Tiles
18. How to use:
• Introduce the unit squares.
• Discuss the idea of unit length, so that the area of the
square is 1.
• Discuss the idea of a negative integer. Note that we can
use the yellow unit squares to represent positive integers
and the violet unit squares to represent negative
integers.
• Show students how two small squares of opposite colors
neutralize each other, so that the net result of such a pair
is zero.
20. Another Pedagogical uses:
• In counting
• In basic operations
• In equality, inequality, and ratios
• In fractions
• In operation of signed numbers
23. Plane Figures
- are flat shapes
- have two dimensions: length and width
- have width and breadth, but no thickness.
24.
25. Area
•The area of a plane figure refers to the number
of square units the figure covers.
•The square units could be inches, centimeters,
yards etc. or whatever the requested unit of
measure asks for.
26. Perimeter
•The distance around a two-dimensional shape.
•The length of the boundary of a closed figure.
• The units of perimeter are same as that of
length, i.e., m, cm, mm, etc.
27. Triangles
A triangle is a closed plane geometric figure formed by
connecting the endpoints of three line segments
endpoint to endpoint.
28. h
b
a c
Perimeter = a + b + c
Area = bh
2
1
The height of a triangle is
measured perpendicular to the
base.
30. b
a h
Perimeter = 2a + 2b
Area = hb Area of a parallelogram
= area of rectangle with
width = h and length = b
31. Rectangle
A rectangle is a quadrilateral that has four right angles.
The opposite sides are parallel to each other. Not all sides
have equal length.
35. Trapezoids
If a quadrilateral has only one pair of opposite sides that
are parallel, then the quadrilateral is a trapezoid. The
parallel sides are called bases. The non-parallel sides are
called legs.
36. Trapezoid
c d
a
b
Perimeter = a + b + c + d
Area =
b
a
Parallelogram with base (a + b) and height = h
with area = h(a + b)
But the trapezoid is half the parallelgram
h(a + b)
2
1
h
37. Circle
A circle is the set of points on a plane that are equidistant
from a fixed point known as the center. A circle is named
by its center.
38. Circle
• A circle is a plane figure in which all points are equidistance from the center.
• The radius, r, is a line segment from the center of the circle to any point on
the circle.
• The diameter, d, is the line segment across the circle through the center. d =
2r
• The circumference, C, of a circle is the distance around the circle. C = 2pr
• The area of a circle is A = pr2.
r
d
39. Find the Circumference
• The circumference, C,
of a circle is the distance
around the circle. C = 2pr
• C = 2pr
• C = 2p(1.5)
• C = 3p cm
1.5 cm
40. Find the Area of the Circle
• The area of a circle is A = pr2
• d=2r
• 8 = 2r
• 4 = r
• A = pr2
• A = p(4)2
• A = 16p sq. in.
8 in
42. Geoboard
Objectives:
The geoboard instructional material will be able to:
• Define polygons
• Solve for the area of polygons
• Solve for the perimeter of polygons
• Visualize the area and perimeter of polygons
• Manipulate the geoboard to find the area and
perimeter of polygons
43. How to use:
• Connect the dots on the geoboard to form a polygon
• Count the connected dots to have the length of the sides
Regular Polygons
To find the perimeter of regular polygons, count all the dots that was
connected.
To find the area of regular polygons, count the square units enclosed by
the connected dots.
Irregular Polygons
To find the perimeter of an irregular polygon, count all the connected
dots.
To find the area of an irregular polygon, visualized a regular polygon
inside the irregular polygon. Use the formulas of the area of regular
48. 19yd
30yd
37yd
23 yd
7yd18yd
What is the perimeter of this irregular polygon?
Find the missing length of other sides.
Add all of the sides up
The perimeter is 134 yd
49. 19yd
30yd
37yd
23yd
7yd
18yd
What is the area of this irregular shape?
Find the area of each rectangle now
133
851
Add the area of the first and second rectangle. The area is 984 sq. yd.
61. • The Platonic Solids, discovered by the Pythagoreans
but described by Plato (in the Timaeus) and used by
him for his theory of the 4 elements, consist of
surfaces of a single kind of regular polygon, with
identical vertices.
62. • The Platonic Solids are named after Plato and were studied
extensively by the ancient Greeks, although he was not the
first to discover them. Plato associated the cube, octahedron,
icosahedron, tetrahedron and dodecahedron with the
elements, earth, wind, water, fire, and the cosmos,
respectively. Crystal Platonic Solids can be used for meditation,
healing, chakra work, grid work, and manifestation. In grid
work, they can be used together, or separately, each as a
center piece in its own crystal grid.
63. Regular Tetrahedron
A regular tetrahedron is a regular polyhedron
composed of 4 equally sized equilateral triangles.
The regular tetrahedron is a regular triangular
pyramid.
64. Characteristics of the Tetrahedron
Number of faces: 4.
Number of vertices: 4.
Number of edges: 6.
Number of concurrent edges at a vertex: 3
72. Regular Octahedron
A regular octahedron is a regular
polyhedron composed of 8 equal equilateral
triangles. The regular octahedron can be
considered to be formed by the union of two
equally sized regular quadrangular pyramids at
their bases.
73. Characteristics of a Octahedron
•Number of faces: 8.
•Number of vertices: 6.
•Number of edges: 12.
•Number of concurrent edges at a vertex: 4.
76. Regular Dodecahedron
• A regular dodecahedron is a regular polyhedron
composed of 12 equally sized regular
pentagons.
77. Characteristics of a Dodecahedron
• Number of faces: 12.
• Number of vertices: 20.
• Number of edges: 30.
• Number of concurrent edges at a vertex: 3.
80. Regular Icosahedron
• A regular icosahedron is a regular polyhedron
composed of 20 equally sized equilateral triangles.
81. Characteristics of an Icosahedron
• Number of faces: 20.
• Number of vertices: 12.
• Number of edges: 30.
• Number of concurrent edges at a vertex: 5.
85. Platonic Solids Model
Objectives:
The platonic solids model instructional material will
be able to:
• Identify platonic solids
• Determine the characteristics of platonic solids
• Differentiate the different kinds platonic solids
• Differentiate Platonic solid and Archimedean solid
87. Archimedean Solids
Model
Objectives:
The archimedean solid model instructional
materials will be able to:
• Identify archimedean solids
• Determine the characteristics of Archimedean solids
• Differentiate the different kinds archimedean solids
• Differentiate archimedean solid and platonic solid
90. Pie Chart
Objectives:
The pie chart instructional material will be able to:
• Define circle
• Solve for the area of a circle
• Solve for the circumference of a circle
• Manipulate the pie chart to find the area and
circumference of a circle
• Manipulate the pie chart to find the relationship
between the area of a circle and a parallelogram
91. How to use:
• Form the whole circle to define the different parts of a circle
• Manipulate the part of the circle to find the relationship of the
radius , diameter and circumference of a circle.
Circle Vs. Parallelogram
• Arrange the part of the pie chart horizontally to form a
parallelogram
• Arrange the part of the pie chart upside down to fill the spaces in
between